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The Journal of Experimental Biology 206, 327-343 (2003)
doi: 10.1242/jeb.00069

The hydrodynamics of locomotion at intermediate Reynolds numbers: undulatory swimming in ascidian larvae (Botrylloides sp.)

Matthew J. McHenry^1,*, Emanuel Azizi² and James A. Strother¹

¹ Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
² Organismic and Evolutionary Biology Program, 221 Morrill Science Center, University of Massachusetts, Amherst, MA 01003, USA

^* Author for correspondence at present address: The Museum of Comparative Zoology, Harvard University, 26 Oxford St, Cambridge, MA 02138, USA (e-mail: mchenry{at}fas.harvard.edu)

Accepted 10 October 2002

Understanding how the shape and motion of an aquatic animal affects the performance of swimming requires knowledge of the fluid forces that generate thrust and drag. These forces are poorly understood for the large diversity of animals that swim at Reynolds numbers (Re) between 10⁰ and 10². We experimentally tested quasi-steady and unsteady blade-element models of the hydrodynamics of undulatory swimming in the larvae of the ascidian Botrylloides sp. by comparing the forces predicted by these models with measured forces generated by tethered larvae and by comparing the swimming speeds predicted with measurements of the speed of freely swimming larvae. Although both models predicted mean forces that were statistically indistinguishable from measurements, the quasi-steady model predicted the timing of force production and mean swimming speed more accurately than the unsteady model. This suggests that unsteady force (i.e. the acceleration reaction) does not play a role in the dynamics of steady undulatory swimming at Re10². We explored the relative contribution of viscous and inertial force to the generation of thrust and drag at 10⁰<Re<10² by running a series of mathematical simulations with the quasi-steady model. These simulations predicted that thrust and drag are dominated by viscous force (i.e. skin friction) at Re10⁰ and that inertial force (i.e. form force) generates a greater proportion of thrust and drag at higher Re than at lower Re. However, thrust was predicted to be generated primarily by inertial force, while drag was predicted to be generated more by viscous than inertial force at Re10². Unlike swimming at high (>10²) and low (<10⁰) Re, the fluid forces that generate thrust cannot be assumed to be the same as those that generate drag at intermediate Re.

Key words: swimming, intermediate Reynolds number, morphology, larvae, ascidian, urochordata, Botrylloides sp

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